Weibel electromagnetic instability has been studied analytically in relativistic plasma with high parallel temperature, where |𝛼 = (𝑚𝑐2/𝑇‖)(1 + 𝑝̂⊥2 /𝑚2𝑐2)1/2| ≪ 1 and while the collision effects of electron-ion scattering have also been considered. According to these conditions, an analytical expression is derived for the growth rate of the Weibel instability for a limiting case of |𝜁 = √𝛼/2(𝜔/𝑐𝑘)| ≪ 1, where 𝜔 is the sum of the wave frequency of instability and the collision frequency of electrons with background ions. The results show that in the limiting condition 𝛼 ≪ 1 there is an unusual situation of the Weibel instability so that 𝑇‖ ≫ 𝑇⊥, while in the classic Weibel instability 𝑇‖ ≪ 𝑇⊥. The obtained results show that the growth rate of the Weibel instability will be decreased due to an increase in the number of collisions and a decrease in the anisotropic temperature by the increasing of plasma density, while the increase of the parameter 𝛾̂⊥ = (1 + 𝑝̂⊥2 /𝑚2𝑐2)1/2 leads to the increase of the Weibel instability growth rate
